Minors of Bezout matrices, subresultants and the parameterization of the degree of the polynomial greatest common divisor

Abstract

The main purpose of this article is to present algorithms to parameterize the degree of the greatest common divisor of two polynomials with parametric coefficients: these algorithms are based on the fact that the principal minors of the Bezout matrices provide the principal subresultant sequence. When coefficients depend on parameters, these algorithms show a better behaviour than the classical ones. E-mail: gemadiaz@um.es E-mail: jounaidi@esstt.rnu.tr